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Detecting spurious signals: hypothesis testing in .NET Generating QR Code ISO/IEC18004 in .NET Detecting spurious signals: hypothesis testing




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2.4 Detecting spurious signals: hypothesis testing generate, create qr barcode none on .net projects ASP.NET Web Application Framework The fundamentals of hypothes VS .NET QR Code 2d barcode is testing. When analyzing patterns in a whole genome we need to consider the possibility that they are a result of chance; this will be more of a problem the bigger a genome gets.

Hence we must devise methods to help us to distinguish reliable patterns from background noise. Measuring the probability of a pattern (such as seeing an open reading frame of a given length) under a null model is a simple and effective way of doing this, though we will often need to make simplifying assumptions about the statistical nature of the underlying DNA sequence. Calculating this probability and making inferences based on it is a fundamental problem in statistics, and is referred to as hypothesis testing.

There are many important, subtle concepts in hypothesis testing, and we cannot cover them all. For the reader unfamiliar with basic hypothesis testing. A L L T H E S E Q U E N C E S M E N : G E N E F I N D I N G we suggest that you refer to VS .NET QR Code JIS X 0510 a general book on probability and statistics; for now we cover the topics that will be essential throughout this book. We consider the data (e.

g. an ORF of a certain length) to be signi cant when it is highly unlikely under the null model. We can never guarantee that the data are not consistent with the null, but we can make a statement about the probability of the observed result arising by chance (called a p-value).

For any test statistic the aspect of the data that we are testing the signi cance of (e.g. ORF length) we must also choose the statistical threshold at which we decide to call our observation signi cant or not signi cant.

This threshold is referred to as , and de nes the probability with which the null hypothesis will be wrongly rejected (an event called a Type I error in statistics, and further discussed below). When our p-value is less than , we consider our data to be signi cant and unlikely to be due to chance. Often a threshold value of = 0.

05 is used to de ne signi cance, a popular (but arbitrary) choice. This value of means that even if the null hypothesis is true, 5% of the time our data will appear to be signi cant. Putting it another way, if our data are signi cant at = 0.

05, it means that we would only have seen a test statistic (e.g. ORF length) as extreme or more extreme than our observed value 5% of the time due to chance alone.

Finding a low p-value for the data, then, gives support for the rejection of the null hypothesis. De nition 2.3 Signi cance level.

The signi cance level of a statistical hypothesis test is a xed probability of wrongly rejecting the null hypothesis H0 , if it is true. The signi cance level is usually denoted by :. Signi cance level = P(Type I error) = .. De nition 2.4 Test statistic .net vs 2010 Quick Response Code .

The test statistic is any aspect of the data that we wish to test the null hypothesis against. We wish to know whether observing our test statistic is likely under the null hypothesis, and if not how unlikely it is to appear by chance. A test statistic can be a value that is directly observable from the data (e.

g. ORF length, or number of Cs in a sequence of some length) or it may be a function of the data (such as a -squared value or other traditional test statistic). De nition 2.

5 p-value. The probability value (p-value) of a statistical hypothesis test is the probability of getting a value of the test statistic as extreme as or more extreme than that observed by chance alone, if the null hypothesis, H0 , is true. It is the probability of wrongly rejecting the null hypothesis if the null is in fact true.

The p-value is compared with the chosen signi cance level and, if it is smaller, the result is signi cant. Remark 2.3 Types of errors in hypothesis testing.

Formally, designing a hypothesis test requires us to de ne a null hypothesis, H0 , and an alternative hypothesis, H1 (e.g. the null hypothesis could be that a given ORF is generated by a random process, the alternative that the ORF has been generated by some biologically.

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